The Estonian striker, who is on loan from Norwegian side Viking, latched on to a ball forward and ran clear of the home defence before finished past goalkeeper Ben Williams with just seven minutes remaining at Easter Road.
The home side were unable to respond in the remaining time, meaning another demoralising defeat after their recent 9-0 aggregate mauling at the hands of Malmo in Europa league qualifying.
Pat Fenlon's side faced an uphill battle from the off, with Ryan McGivern, James McPake, Jordon Forster, Tim Clancy, Paul Cairney and Rowan Vine all unavailable through injury or suspension.
The visitors created the better chances in the first half as Keith Lasley saw a left-footed effort saved and Bob McHugh put a header narrowly wide of goal.
Motherwell keeper Lee Hollis made his first save five minutes into the second half when he comfortably held Liam Craig's driven free-kick.
This prompted a much better period for Hibs, for whom Kevin Thomson had a long-range effort saved before Hollis pushed Scott Robertson's well-executed first-time volley over the bar.
Hibs needed Williams to be alert to make two excellent saves with 13 minutes left and again soon after when he got down well to push John Sutton's shot just past the post.
But the keeper was unable to come to their rescue shortly after as Anier pounced to seal the game in Motherwell's favour and put further pressure on Hibs boss Fenlon ahead of next week's derby with Hearts.